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Arroyo‐Cosultchi G, Golubov J, Mandujano MC, Salguero‐Gómez R, Martínez AJ. What are the demographic consequences of a seed bank stage for columnar cacti? POPUL ECOL 2021. [DOI: 10.1002/1438-390x.12096] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Gabriel Arroyo‐Cosultchi
- Departamento El Hombre y su Ambiente Universidad Autónoma Metropolitana Xochimilco México Mexico
| | - Jordan Golubov
- Departamento El Hombre y su Ambiente Universidad Autónoma Metropolitana Xochimilco México Mexico
| | - María C. Mandujano
- Instituto de Ecología, Departamento de Ecología de la Biodiversidad, Laboratorio de Genética y Ecología Universidad Nacional Autónoma de México México Mexico
| | - Roberto Salguero‐Gómez
- Department of Zoology University of Oxford Oxford UK
- School of Biological Sciences, Centre for Biodiversity and Conservation Science The University of Queensland St Lucia Queensland Australia
- Laboratory of Evolutionary Demography Max Planck Institute for Demographic Research Rostock Germany
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2
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Logofet DO, Salguero-Gómez R. Novel challenges and opportunities in the theory and practice of matrix population modelling: An editorial for the special feature. Ecol Modell 2021. [DOI: 10.1016/j.ecolmodel.2021.109457] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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3
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Rose JP, Todd BD. Targeting eradication of introduced watersnakes using integral projection models. Anim Conserv 2020. [DOI: 10.1111/acv.12590] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
| | - Brian D. Todd
- Department of Wildlife, Fish, and Conservation Biology University of California Davis CA USA
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4
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Coste CF, Pavard S. Analysis of a multitrait population projection matrix reveals the evolutionary and demographic effects of a life history trade-off. Ecol Modell 2020. [DOI: 10.1016/j.ecolmodel.2019.108915] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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5
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Pilowsky JA, Dahlgren JP. Incorporating the temporal autocorrelation of demographic rates into structured population models. OIKOS 2019. [DOI: 10.1111/oik.06438] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Julia A. Pilowsky
- Dept of Ecology and Evolutionary Biology, Univ. of Adelaide, Benham Laboratories North Terrace Campus AU‐5005 Adelaide South Australia Australia
- Center for Macroecology, Evolution and Climate, Univ. of Copenhagen Universitetsparken 15 DK‐2100 7 Copenhagen Denmark
| | - Johan P. Dahlgren
- Dept of Biology, SDU Interdisciplinary Centre on Population Dynamics, Univ. of Southern Denmark Odense Denmark
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6
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Rose JP, Ersan JSM, Wylie GD, Casazza ML, Halstead BJ. Demographic factors affecting population growth in giant gartersnakes. J Wildl Manage 2019. [DOI: 10.1002/jwmg.21728] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Jonathan P. Rose
- U.S. Geological Survey, Western Ecological Research Center, Dixon Field Station, 800 Business Park Dr, Suite DDixon CA 95620 USA
| | - Julia S. M. Ersan
- U.S. Geological Survey, Western Ecological Research Center, Dixon Field Station, 800 Business Park Dr, Suite DDixon CA 95620 USA
| | - Glenn D. Wylie
- U.S. Geological Survey, Western Ecological Research Center, Dixon Field Station, 800 Business Park Dr, Suite DDixon CA 95620 USA
| | - Michael L. Casazza
- U.S. Geological Survey, Western Ecological Research Center, Dixon Field Station, 800 Business Park Dr, Suite DDixon CA 95620 USA
| | - Brian J. Halstead
- U.S. Geological Survey, Western Ecological Research Center, Dixon Field Station, 800 Business Park Dr, Suite DDixon CA 95620 USA
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7
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Werner PA, Peacock SJ. Savanna canopy trees under fire: long‐term persistence and transient dynamics from a stage‐based matrix population model. Ecosphere 2019. [DOI: 10.1002/ecs2.2706] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022] Open
Affiliation(s)
- Patricia A. Werner
- Fenner School of Environment and Society Australian National University Bldg 141 Linnaeus Way Canberra Australian Capital Territory 0200 Australia
| | - Stephanie J. Peacock
- Ecology and Evolutionary Biology University of Toronto 25 Willcocks Street Toronto Ontario M5S 3B2 Canada
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8
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Takada T, Kawai Y, Salguero‐Gómez R. A cautionary note on elasticity analyses in a ternary plot using randomly generated population matrices. POPUL ECOL 2018. [DOI: 10.1007/s10144-018-0619-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Takenori Takada
- Graduate School of Environmental ScienceHokkaido UniversityKita‐ku060‐0810SapporoJapan
| | - Yuka Kawai
- Graduate School of Environmental ScienceHokkaido UniversityKita‐ku060‐0810SapporoJapan
| | - Roberto Salguero‐Gómez
- Department of ZoologyOxford UniversityNew Radcliffe House, Radcliffe Observatory Quarter, 6GG, Woodstock RdOX2OxfordUK
- Centre for Biodiversity and Conservation ScienceUniversity of Queensland4071St. LuciaQLDAustralia
- Evolutionary Demography LaboratoryMax Plank Institute for Demographic Research18057RostockGermany
- Department of Animal and Plant SciencesUniversity of SheffieldAlfred Denny Building, Western BankS10 2TNSheffieldUK
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9
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Coste CFD, Austerlitz F, Pavard S. Trait level analysis of multitrait population projection matrices. Theor Popul Biol 2017; 116:47-58. [PMID: 28757374 DOI: 10.1016/j.tpb.2017.07.002] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2016] [Revised: 07/05/2017] [Accepted: 07/10/2017] [Indexed: 11/30/2022]
Abstract
In most matrix population projection models, individuals are characterized according to, usually, one or two traits such as age, stage, size or location. A broad theory of multitrait population projection matrices (MPPMs) incorporating larger number of traits was long held back by time and space computational complexity issues. As a consequence, no study has yet focused on the influence of the structure of traits describing a life-cycle on population dynamics and life-history evolution. We present here a novel vector-based MPPM building methodology that allows to computationally-efficiently model populations characterized by numerous traits with large distributions, and extend sensitivity analyses for these models. We then present a new method, the trait level analysis consisting in folding an MPPM on any of its traits to create a matrix with alternative trait structure (the number of traits and their characteristics) but similar asymptotic properties. Adding or removing one or several traits to/from the MPPM and analyzing the resulting changes in spectral properties, allows investigating the influence of the trait structure on the evolution of traits. We illustrate this by modeling a 3-trait (age, parity and fecundity) population designed to investigate the implications of parity-fertilitytrade-offs in a context of fecundity heterogeneity in humans. The trait level analysis, comparing models of the same population differing in trait structures, demonstrates that fertility selection gradients differ between cases with or without parity-fertility trade-offs. Moreover it shows that age-specific fertility has seemingly very different evolutionary significance depending on whether heterogeneity is accounted for. This is because trade-offs can vary strongly in strength and even direction depending on the trait structure used to model the population.
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Affiliation(s)
- Christophe F D Coste
- UMR 7206 EcoAnthropologie et Ethnobiologie, MNHN, Université Paris Diderot, F-75016, Paris, France.
| | - Frédéric Austerlitz
- UMR 7206 EcoAnthropologie et Ethnobiologie, MNHN, Université Paris Diderot, F-75016, Paris, France
| | - Samuel Pavard
- UMR 7206 EcoAnthropologie et Ethnobiologie, MNHN, Université Paris Diderot, F-75016, Paris, France
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10
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Bienvenu F, Akçay E, Legendre S, McCandlish DM. The genealogical decomposition of a matrix population model with applications to the aggregation of stages. Theor Popul Biol 2017; 115:69-80. [PMID: 28476403 DOI: 10.1016/j.tpb.2017.04.002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2016] [Revised: 04/19/2017] [Accepted: 04/26/2017] [Indexed: 10/19/2022]
Abstract
Matrix projection models are a central tool in many areas of population biology. In most applications, one starts from the projection matrix to quantify the asymptotic growth rate of the population (the dominant eigenvalue), the stable stage distribution, and the reproductive values (the dominant right and left eigenvectors, respectively). Any primitive projection matrix also has an associated ergodic Markov chain that contains information about the genealogy of the population. In this paper, we show that these facts can be used to specify any matrix population model as a triple consisting of the ergodic Markov matrix, the dominant eigenvalue and one of the corresponding eigenvectors. This decomposition of the projection matrix separates properties associated with lineages from those associated with individuals. It also clarifies the relationships between many quantities commonly used to describe such models, including the relationship between eigenvalue sensitivities and elasticities. We illustrate the utility of such a decomposition by introducing a new method for aggregating classes in a matrix population model to produce a simpler model with a smaller number of classes. Unlike the standard method, our method has the advantage of preserving reproductive values and elasticities. It also has conceptually satisfying properties such as commuting with changes of units.
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Affiliation(s)
- François Bienvenu
- Institut de Biologie de l'Ecole Normale Supérieure (IBENS), CNRS, INSERM, Ecole Normale Supérieure, PSL Research University, F-75005 Paris, France; University of Pennsylvania Biology Department, Philadelphia, PA 19104, USA; Center for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS, INSERM, PSL Research University, F-75005 Paris, France.
| | - Erol Akçay
- University of Pennsylvania Biology Department, Philadelphia, PA 19104, USA
| | - Stéphane Legendre
- Institut de Biologie de l'Ecole Normale Supérieure (IBENS), CNRS, INSERM, Ecole Normale Supérieure, PSL Research University, F-75005 Paris, France
| | - David M McCandlish
- University of Pennsylvania Biology Department, Philadelphia, PA 19104, USA; Simons Center for Quantitative Biology, Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724, USA.
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11
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Coutts SR, Salguero-Gómez R, Csergő AM, Buckley YM. Extrapolating demography with climate, proximity and phylogeny: approach with caution. Ecol Lett 2016; 19:1429-1438. [PMID: 27790817 DOI: 10.1111/ele.12691] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2016] [Revised: 09/07/2016] [Accepted: 09/18/2016] [Indexed: 11/26/2022]
Abstract
Plant population responses are key to understanding the effects of threats such as climate change and invasions. However, we lack demographic data for most species, and the data we have are often geographically aggregated. We determined to what extent existing data can be extrapolated to predict population performance across larger sets of species and spatial areas. We used 550 matrix models, across 210 species, sourced from the COMPADRE Plant Matrix Database, to model how climate, geographic proximity and phylogeny predicted population performance. Models including only geographic proximity and phylogeny explained 5-40% of the variation in four key metrics of population performance. However, there was poor extrapolation between species and extrapolation was limited to geographic scales smaller than those at which landscape scale threats typically occur. Thus, demographic information should only be extrapolated with caution. Capturing demography at scales relevant to landscape level threats will require more geographically extensive sampling.
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Affiliation(s)
- Shaun R Coutts
- School of Biological Sciences, Centre for Biodiversity and Conservation Science, The University of Queensland, St Lucia, Qld., 4072, Australia.,Department of Animal and Plant Sciences, University of Sheffield, Western Bank, Sheffield, UK.,School of Natural Sciences, Zoology, Trinity College Dublin, Dublin 2, Ireland
| | - Roberto Salguero-Gómez
- School of Biological Sciences, Centre for Biodiversity and Conservation Science, The University of Queensland, St Lucia, Qld., 4072, Australia.,Department of Animal and Plant Sciences, University of Sheffield, Western Bank, Sheffield, UK.,School of Natural Sciences, Zoology, Trinity College Dublin, Dublin 2, Ireland.,Evolutionary Demography Laboratory, Max Planck Institute for Demographic Research, Rostock, DE-18057, Germany
| | - Anna M Csergő
- School of Natural Sciences, Zoology, Trinity College Dublin, Dublin 2, Ireland
| | - Yvonne M Buckley
- School of Biological Sciences, Centre for Biodiversity and Conservation Science, The University of Queensland, St Lucia, Qld., 4072, Australia.,School of Natural Sciences, Zoology, Trinity College Dublin, Dublin 2, Ireland
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12
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Population viability analysis of plant and animal populations with stochastic integral projection models. Oecologia 2016; 182:1031-1043. [DOI: 10.1007/s00442-016-3704-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2014] [Accepted: 08/10/2016] [Indexed: 10/21/2022]
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Tremblay RL, Raventos J, Ackerman JD. When stable-stage equilibrium is unlikely: integrating transient population dynamics improves asymptotic methods. ANNALS OF BOTANY 2015; 116:381-90. [PMID: 25814059 PMCID: PMC4549953 DOI: 10.1093/aob/mcv031] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2014] [Accepted: 02/04/2015] [Indexed: 05/13/2023]
Abstract
BACKGROUND AND AIMS Evaluation of population projection matrices (PPMs) that are focused on asymptotically based properties of populations is a commonly used approach to evaluate projected dynamics of managed populations. Recently, a set of tools for evaluating the properties of transient dynamics has been expanded to evaluate PPMs and to consider the dynamics of populations prior to attaining the stable-stage distribution, a state that may never be achieved in disturbed or otherwise ephemeral habitats or persistently small populations. This study re-evaluates data for a tropical orchid and examines the value of including such analyses in an integrative approach. METHODS Six small populations of Lepanthes rubripetala were used as a model system and the R software package popdemo was used to produce estimates of the indices for the asymptotic growth rate (lambda), sensitivities, reactivity, first-time step attenuation, maximum amplification, maximum attenuation, maximal inertia and maximal attenuation. The response in lambda to perturbations of demographic parameters using transfer functions and multiple perturbations on growth, stasis and fecundity were also determined. The results were compared with previously published asymptotic indices. KEY RESULTS It was found that combining asymptotic and transient dynamics expands the understanding of possible population changes. Comparison of the predicted density from reactivity and first-time step attenuation with the observed change in population size in two orchid populations showed that the observed density was within the predicted range. However, transfer function analysis suggests that the traditional approach of measuring perturbation of growth rates and persistence (inertia) may be misleading and is likely to result in erroneous management decisions. CONCLUSIONS Based on the results, an integrative approach is recommended using traditional PPMs (asymptotic processes) with an evaluation of the diversity of dynamics that may arise when populations are not at a stable-stage distribution (transient processes). This method is preferable for designing rapid and efficient interventions after disturbances, and for developing strategies to establish new populations.
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Affiliation(s)
- Raymond L Tremblay
- Department of Biology, PO Box 860, University of Puerto Rico, Humacao, 00791, Puerto Rico,
| | - Josep Raventos
- Departamento de Ecología, Universidad de Alicante, Carretera S. Vicente del Raspeig s/n, 03080, San Vicente del Raspeig, Alicante, Spain
| | - James D Ackerman
- Department of Biology, PO Box 23360, University of Puerto Rico, Rio Piedras campus, San Juan, 00931-3360, Puerto Rico, Center for Applied Tropical Ecology and Conservation, PO Box 23360, University of Puerto Rico, Rio Piedras campus, San Juan, 00931-3360, Puerto Rico and
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Picard N, Liang J. Matrix models for size-structured populations: unrealistic fast growth or simply diffusion? PLoS One 2014; 9:e98254. [PMID: 24905941 PMCID: PMC4048208 DOI: 10.1371/journal.pone.0098254] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2014] [Accepted: 04/29/2014] [Indexed: 12/02/2022] Open
Abstract
Matrix population models are widely used to study population dynamics but have been criticized because their outputs are sensitive to the dimension of the matrix (or, equivalently, to the class width). This sensitivity is concerning for the population growth rate (λ) because this is an intrinsic characteristic of the population that should not depend on the model specification. It has been suggested that the sensitivity of λ to matrix dimension was linked to the existence of fast pathways (i.e. the fraction of individuals that systematically move up a class), whose proportion increases when class width increases. We showed that for matrix population models with growth transition only from class i to class i + 1, λ was independent of the class width when the mortality and the recruitment rates were constant, irrespective of the growth rate. We also showed that if there were indeed fast pathways, there were also in about the same proportion slow pathways (i.e. the fraction of individuals that systematically remained in the same class), and that they jointly act as a diffusion process (where diffusion here is the movement in size of an individual whose size increments are random according to a normal distribution with mean zero). For 53 tree species from a tropical rain forest in the Central African Republic, the diffusion resulting from common matrix dimensions was much stronger than would be realistic. Yet, the sensitivity of λ to matrix dimension for a class width in the range 1-10 cm was small, much smaller than the sampling uncertainty on the value of λ. Moreover, λ could either increase or decrease when class width increased depending on the species. Overall, even if the class width should be kept small enough to limit diffusion, it had little impact on the estimate of λ for tree species.
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Affiliation(s)
- Nicolas Picard
- UPR Biens et services des écosystèmes forestiers tropicaux (BSEF), Centre de coopération internationale en recherche agronomique pour le développement (CIRAD), Montpellier, France
| | - Jingjing Liang
- Division of Forestry and Natural Resources, West Virginia University, Morgantown, West Virginia, United States of America
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Ibrahim L, Preuss TG, Schaeffer A, Hommen U. A contribution to the identification of representative vulnerable fish species for pesticide risk assessment in Europe—A comparison of population resilience using matrix models. Ecol Modell 2014. [DOI: 10.1016/j.ecolmodel.2013.08.001] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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16
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Abstract
Ecologists seek general explanations for the dramatic variation in species abundances in space and time. An increasingly popular solution is to predict species distributions, dynamics, and responses to environmental change based on easily measured anatomical and morphological traits. Trait-based approaches assume that simple functional traits influence fitness and life history evolution, but rigorous tests of this assumption are lacking, because they require quantitative information about the full lifecycles of many species representing different life histories. Here, we link a global traits database with empirical matrix population models for 222 species and report strong relationships between functional traits and plant life histories. Species with large seeds, long-lived leaves, or dense wood have slow life histories, with mean fitness (i.e., population growth rates) more strongly influenced by survival than by growth or fecundity, compared with fast life history species with small seeds, short-lived leaves, or soft wood. In contrast to measures of demographic contributions to fitness based on whole lifecycles, analyses focused on raw demographic rates may underestimate the strength of association between traits and mean fitness. Our results help establish the physiological basis for plant life history evolution and show the potential for trait-based approaches in population dynamics.
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Rojas-Sandoval J, Meléndez-Ackerman E. Population dynamics of a threatened cactus species: general assessment and effects of matrix dimensionality. POPUL ECOL 2013. [DOI: 10.1007/s10144-013-0378-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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18
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Enright NJ, Miller BP, Perry GLW, Goldblum D, Jaffré T. Stress-tolerator leaf traits determine population dynamics in the endangered New Caledonian coniferAraucaria muelleri. AUSTRAL ECOL 2013. [DOI: 10.1111/aec.12045] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Neal J. Enright
- School of Veterinary and Life Sciences; Murdoch University; Murdoch Perth WA 6150
| | - Ben P. Miller
- Botanical Gardens and Parks Authority; West Perth
- School of Plant Biology; University of Western Australia; Nedlands Western Australia Australia
| | - George L. W. Perry
- Schools of Environment; University of Auckland; Auckland New Zealand
- Biological Sciences; University of Auckland; Auckland New Zealand
| | - David Goldblum
- Department of Geography; Northern Illinois University; DeKalb USA
| | - Tanguy Jaffré
- UMR-AMAP, IRD: Institut de Recherche pour le Développement; Laboratoire de Botanique et d'Ecologie Végétale; Nouméa New Caledonia
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Comments on: Inference for Size Demography From Point Pattern Data Using Integral Projection Models. JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS 2012. [DOI: 10.1007/s13253-012-0120-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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González EJ, Rees M, Martorell C. Identifying the demographic processes relevant for species conservation in human-impacted areas: does the model matter? Oecologia 2012; 171:347-56. [PMID: 22955702 DOI: 10.1007/s00442-012-2432-7] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2011] [Accepted: 08/06/2012] [Indexed: 11/28/2022]
Abstract
The identification of the demographic processes responsible for the decline in population growth rate (λ) in disturbed areas would allow conservation efforts to be efficiently directed. Integral projection models (IPMs) are used for this purpose, but it is unclear whether the conclusions drawn from their analysis are sensitive to how functional structures (the functions that describe how survival, growth and fecundity vary with individual size) are selected. We constructed 12 IPMs that differed in their functional structure by combining two reproduction models and three functional expressions (generalized linear, cubic and additive models), each with and without simplification. Models were parameterized with data from two populations of two endangered cacti subject to different disturbance intensities. For each model, we identified the demographic processes that most affected λ in the presence of disturbance. Simulations were performed on artificial data and analyzed as above to assess the generality of the results. In both empirical and simulated data, the same processes were identified as making the largest contribution to changes in λ regardless of the functional structure. The major differences in the results were due to misspecification of the fecundity functions, whilst functional expression and model simplification had lesser effects. Therefore, as long as the demographic attributes of the species are well known and incorporated into the model, IPMs will robustly identify the processes that most affect the growth of populations subject to disturbance, making them a reliable tool for developing conservation strategies.
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Affiliation(s)
- Edgar J González
- Departamento de Ecología y Recursos Naturales, Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Exterior s/n, Ciudad Universitaria, 04510, Mexico, D.F., Mexico.
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Ferrer-Cervantes ME, Méndez-González ME, Quintana-Ascencio PF, Dorantes A, Dzib G, Durán R. Population dynamics of the cactus Mammillaria gaumeri: an integral projection model approach. POPUL ECOL 2012. [DOI: 10.1007/s10144-012-0308-7] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Shefferson RP, Kull T, Tali K, Kellett KM. Linking vegetative dormancy to fitness in two long-lived herbaceous perennials. Ecosphere 2012. [DOI: 10.1890/es11-00328.1] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
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23
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Che-Castaldo JP, Inouye DW. The effects of dataset length and mast seeding on the demography ofFrasera speciosa, a long-lived monocarpic plant. Ecosphere 2011. [DOI: 10.1890/es11-00263.1] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
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Jongejans E, Shea K, Skarpaas O, Kelly D, Ellner SP. Importance of individual and environmental variation for invasive species spread: a spatial integral projection model. Ecology 2011; 92:86-97. [DOI: 10.1890/09-2226.1] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Salguero-Gómez R, Plotkin JB. Matrix dimensions bias demographic inferences: implications for comparative plant demography. Am Nat 2010; 176:710-22. [PMID: 20964622 DOI: 10.1086/657044] [Citation(s) in RCA: 66] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
While the wealth of projection matrices in plant demography permits comparative studies, variation in matrix dimensions complicates interspecific comparisons. Collapsing matrices to a common dimension may facilitate such comparisons but may also bias the inferred demographic parameters. Here we examine how matrix dimension affects inferred demographic elasticities and how different collapsing criteria perform. We analyzed 13 x 13 matrices representing nine plant species, collapsing these matrices (i) into even 7 x 7, 5 x 5, 4 x 4, and 3 x 3 matrices and (ii) into 5 x 5 matrices using different criteria. Stasis and fecundity elasticities increased when matrix dimension was reduced, whereas those of progression and retrogression decreased. We suggest a collapsing criterion that minimizes dissimilarities between the original- and collapsed-matrix elasticities and apply it to 66 plant species to study how life span and growth form influence the relationship between matrix dimension and elasticities. Our analysis demonstrates that (i) projection matrix dimension has significant effects on inferred demographic parameters, (ii) there are better-performing methods than previously suggested for standardizing matrix dimension, and (iii) herbaceous perennial projection matrices are particularly sensitive to changes in matrix dimensionality. For comparative demographic studies, we recommend normalizing matrices to a common dimension by collapsing higher classes and leaving the first few classes unaltered.
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Bassar RD, López-Sepulcre A, Walsh MR, Turcotte MM, Torres-Mejia M, Reznick DN. Bridging the gap between ecology and evolution: integrating density regulation and life-history evolution. Ann N Y Acad Sci 2010; 1206:17-34. [DOI: 10.1111/j.1749-6632.2010.05706.x] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Synergy of multiple partners, including freeloaders, increases host fitness in a multispecies mutualism. Proc Natl Acad Sci U S A 2010; 107:17234-9. [PMID: 20855614 DOI: 10.1073/pnas.1006872107] [Citation(s) in RCA: 140] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Understanding cooperation is a central challenge in biology, because natural selection should favor "free-loaders" that reap benefits without reciprocating. For interspecific cooperation (mutualism), most approaches to this paradox focus on costs and benefits of individual partners and the strategies mutualists use to associate with beneficial partners. However, natural selection acts on lifetime fitness, and most mutualists, particularly longer-lived species interacting with shorter-lived partners (e.g., corals and zooxanthellae, tropical trees and mycorrhizae) interact with multiple partner species throughout ontogeny. Determining how multiple partnerships might interactively affect lifetime fitness is a crucial unexplored link in understanding the evolution and maintenance of cooperation. The tropical tree Acacia drepanolobium associates with four symbiotic ant species whose short-term individual effects range from mutualistic to parasitic. Using a long-term dataset, we show that tree fitness is enhanced by partnering sequentially with sets of different ant symbionts over the ontogeny of a tree. These sets include a "sterilization parasite" that prevents reproduction and another that reduces tree survivorship. Trees associating with partner sets that include these "parasites" enhance lifetime fitness by trading off survivorship and fecundity at different life stages. Our results demonstrate the importance of evaluating mutualism within a community context and suggest that lifespan inequalities among mutualists may help cooperation persist in the face of exploitation.
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Stott I, Townley S, Carslake D, Hodgson DJ. On reducibility and ergodicity of population projection matrix models. Methods Ecol Evol 2010. [DOI: 10.1111/j.2041-210x.2010.00032.x] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Shelton AO. The Ecological and Evolutionary Drivers of Female‐Biased Sex Ratios: Two‐Sex Models of Perennial Seagrasses. Am Nat 2010; 175:302-15. [PMID: 20109068 DOI: 10.1086/650374] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Andrew Olaf Shelton
- Department of Ecology and Evolution, University of Chicago, Chicago, Illinois 60637, USA.
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Rigg LS, Enright NJ, Jaffré T, Perry GLW. Contrasting Population Dynamics of the Endemic New Caledonian Conifer Araucaria laubenfelsii in Maquis and Rain Forest. Biotropica 2010. [DOI: 10.1111/j.1744-7429.2009.00615.x] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Carslake D, Townley S, Hodgson DJ. Patterns and rules for sensitivity and elasticity in population projection matrices. Ecology 2010; 90:3258-67. [PMID: 19967880 DOI: 10.1890/08-1188.1] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Sensitivity and elasticity analysis of population projection matrices (PPMs) are established tools in the analysis of structured populations, allowing comparison of the contributions made by different demographic rates to population growth. In some commonly used structures of PPM, however, there are mathematically inevitable patterns in the relative sensitivity and elasticity of certain demographic rates. We take a simulation approach to investigate these mathematical constraints for a range of PPM models. Our results challenge some previously proposed constraints on sensitivity and elasticity. We also identify constraints beyond those that have already been proven mathematically and promote them as candidates for future mathematical proof. A general theme among these rules is that changes to the demographic rates of older or larger individuals have less impact on population growth than do equivalent changes among younger or smaller individuals. However, the validity of these rules in each case depends on the choice between sensitivity and elasticity, the growth rate of the population, and the PPM structure used. If the structured population conforms perfectly to the assumptions of the PPM used to model it, the rules we describe represent biological reality, allowing us to prioritize management strategies in the absence of detailed demographic data. Conversely, if the model is a poor fit to the population (specifically, if demographic rates within stages are heterogeneous), such analyses could lead to inappropriate management prescriptions. Our results emphasize the importance of choosing a structured population model that fits the demographics of the population.
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Affiliation(s)
- David Carslake
- Centre for Ecology and Conservation, University of Exeter, Tremough Campus, Penryn, Cornwall TR10 9EZ, United Kingdom.
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Abe S, Motai H, Tanaka H, Shibata M, Kominami Y, Nakashizuka T. Population maintenance of the short-lived shrub Sambucus in a deciduous forest. Ecology 2008; 89:1155-67. [PMID: 18481539 DOI: 10.1890/06-2009.1] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This study quantitatively clarifies the life history of a shrub, Sambucus racemosa ssp. sieboldiana, in an old-growth forest, the Ogawa Forest Reserve, Japan, by a demographic approach using a projection matrix model that incorporates interactions between demographic parameters and canopy height dynamics. S. racemosa is a common deciduous shrub in central Japan and is known to grow predominantly at forest edges or roadsides. This indicates that it is a highly light-demanding species, and occurrence in gaps in old-growth stands suggests its "fugitive," gap-dependent life history in old-growth forests. We found that one distinctive feature of this species was that its seedlings can survive well in shaded conditions by alternating stems every year like perennial herb species. Matrix model analyses demonstrated that S. racemosa can continuously regenerate under the present disturbance regime of this forest and is highly adaptable to the structural dynamics of the old-growth forest. The maturity of S. racemosa shrubs depends on their size, and nearly all (>90%) of the mature (reproducing) individuals were found in gaps or near gaps. But wide seed dispersal by birds and the ability to form both seed banks and seedling banks, the latter of which has been regarded as a common characteristic of shade-tolerant climax species, probably increase the species' chances to encounter canopy gaps. Dynamic-canopied matrix models showed that the greatest elasticity is with shaded seedling survival. The frequent stem alternation of shaded seedlings often makes the growth rate negative, but the survival rate of seedlings in low light awaiting new gap creation is remarkably high (0.93 yr(-1)). The lower survival rate of the larger individuals and smaller minimum size to start reproduction than other canopy or subcanopy shade-tolerant species indicate that S. racemosa has the potential to reproduce before the closure of the encountered gaps and to complete its life history rapidly.
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Affiliation(s)
- Shin Abe
- Forestry and Forest Products Research Institute, Matsunosato 1, Tsukuba 305-8687, Ibaraki, Japan.
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34
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Ramula S, Knight TM, Burns JH, Buckley YM. General guidelines for invasive plant management based on comparative demography of invasive and native plant populations. J Appl Ecol 2008. [DOI: 10.1111/j.1365-2664.2008.01502.x] [Citation(s) in RCA: 138] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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35
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Ripley BJ, Caswell H. Contributions of growth, stasis, and reproduction to fitness in brooding and broadcast spawning marine bivalves. POPUL ECOL 2008. [DOI: 10.1007/s10144-008-0075-7] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Benton TG, Plaistow SJ, Coulson TN. Complex population dynamics and complex causation: devils, details and demography. Proc Biol Sci 2006; 273:1173-81. [PMID: 16720388 PMCID: PMC1560275 DOI: 10.1098/rspb.2006.3495] [Citation(s) in RCA: 181] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2005] [Accepted: 01/23/2006] [Indexed: 11/12/2022] Open
Abstract
Population dynamics result from the interplay of density-independent and density-dependent processes. Understanding this interplay is important, especially for being able to predict near-term population trajectories for management. In recent years, the study of model systems-experimental, observational and theoretical-has shed considerable light on the way that the both density-dependent and -independent aspects of the environment affect population dynamics via impacting on the organism's life history and therefore demography. These model-based approaches suggest that (i) individuals in different states differ in their demographic performance, (ii) these differences generate structure that can fluctuate independently of current total population size and so can influence the dynamics in important ways, (iii) individuals are strongly affected by both current and past environments, even when the past environments may be in previous generations and (iv) dynamics are typically complex and transient due to environmental noise perturbing complex population structures. For understanding population dynamics of any given system, we suggest that 'the devil is in the detail'. Experimental dissection of empirical systems is providing important insights into the details of the drivers of demographic responses and therefore dynamics and should also stimulate theory that incorporates relevant biological mechanism.
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Affiliation(s)
- Tim G Benton
- University of Leeds Institute of Integrative and Comparative Biology Leeds LS2 9JT, UK.
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38
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PFEIFER MARION, WIEGAND KERSTIN, HEINRICH WOLFGANG, JETSCHKE GOTTFRIED. Long-term demographic fluctuations in an orchid species driven by weather: implications for conservation planning. J Appl Ecol 2006. [DOI: 10.1111/j.1365-2664.2006.01148.x] [Citation(s) in RCA: 67] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Ellner SP, Rees M. Integral projection models for species with complex demography. Am Nat 2006; 167:410-28. [PMID: 16673349 DOI: 10.1086/499438] [Citation(s) in RCA: 416] [Impact Index Per Article: 23.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2005] [Accepted: 10/27/2005] [Indexed: 11/03/2022]
Abstract
Matrix projection models occupy a central role in population and conservation biology. Matrix models divide a population into discrete classes, even if the structuring trait exhibits continuous variation (e.g., body size). The integral projection model (IPM) avoids discrete classes and potential artifacts from arbitrary class divisions, facilitates parsimonious modeling based on smooth relationships between individual state and demographic performance, and can be implemented with standard matrix software. Here, we extend the IPM to species with complex demographic attributes, including dormant and active life stages, cross-classification by several attributes (e.g., size, age, and condition), and changes between discrete and continuous structure over the life cycle. We present a general model encompassing these cases, numerical methods, and theoretical results, including stable population growth and sensitivity/elasticity analysis for density-independent models, local stability analysis in density-dependent models, and optimal/evolutionarily stable strategy life-history analysis. Our presentation centers on an IPM for the thistle Onopordum illyricum based on a 6-year field study. Flowering and death probabilities are size and age dependent, and individuals also vary in a latent attribute affecting survival, but a predictively accurate IPM is completely parameterized by fitting a few regression equations. The online edition of the American Naturalist includes a zip archive of R scripts illustrating our suggested methods.A zip archive of R scripts illustrating our suggested methods is also provided.
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Affiliation(s)
- Stephen P Ellner
- Department of Ecology and Evolutionary Biology, Cornell University, Ithaca, New York, 24853, USA.
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40
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Rogers-Bennett L, Leaf RT. Elasticity analyses of size-based red and white abalone matrix models: management and conservation. ECOLOGICAL APPLICATIONS : A PUBLICATION OF THE ECOLOGICAL SOCIETY OF AMERICA 2006; 16:213-24. [PMID: 16705974 DOI: 10.1890/04-1688] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
Prospective elasticity analyses have been used to aid in the management of fished species and the conservation of endangered species. Elasticities were examined for deterministic size-based matrix models of red abalone, Haliotis rufescens, and white abalone, H. sorenseni, to evaluate which size classes influenced population growth (lambda) the most. In the red abalone matrix, growth transitions were determined from a tag recapture study and grouped into nine size classes. In the white abalone matrix, abalone growth was determined from a laboratory study and grouped into five size classes. Survivorship was estimated from tag recapture data for red abalone using a Jolly-Seber model with size as a covariate and used for both red and white abalone. Reproduction estimates for both models used averages of the number of mature eggs produced by female red and white abalone in each size class from four-year reproduction studies. Population growth rate (lambda) was set to 1.0, and the first-year survival (larval survival through to the first size class) was estimated by iteration. Survival elasticities were higher than fecundity elasticities in both the red and white matrix models. The sizes classes with the greatest survival elasticities, and therefore the most influence on population growth in the model, were the sublegal red abalone (150-178 mm) and the largest white abalone size class (140-175 mm). For red abalone, the existing minimum legal size (178 mm) protects the size class the model suggests is critical to population growth. Implementation of education programs for novice divers coupled with renewed enforcement may serve to minimize incidental mortality of the critical size class. For white abalone, conservation efforts directed at restoring adults may have more of an impact on population growth than efforts focusing on juveniles. Our work is an example of how prospective elasticity analyses of size-structured matrix models can be used to quantitatively evaluate research priorities, fishery management strategies, and conservation options.
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Affiliation(s)
- Laura Rogers-Bennett
- California Department of Fish and Game, University of California-Davis, Bodega Marine Laboratory, 2099 Westside Rd., Bodega Bay, California 94923-0247, USA.
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Gotelli NJ, Ellison AM. Forecasting extinction risk with nonstationary matrix models. ECOLOGICAL APPLICATIONS : A PUBLICATION OF THE ECOLOGICAL SOCIETY OF AMERICA 2006; 16:51-61. [PMID: 16705960 DOI: 10.1890/04-0479] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
Matrix population growth models are standard tools for forecasting population change and for managing rare species, but they are less useful for predicting extinction risk in the face of changing environmental conditions. Deterministic models provide point estimates of lambda, the finite rate of increase, as well as measures of matrix sensitivity and elasticity. Stationary matrix models can be used to estimate extinction risk in a variable environment, but they assume that the matrix elements are randomly sampled from a stationary (i.e., non-changing) distribution. Here we outline a method for using nonstationary matrix models to construct realistic forecasts of population fluctuation in changing environments. Our method requires three pieces of data: (1) field estimates of transition matrix elements, (2) experimental data on the demographic responses of populations to altered environmental conditions, and (3) forecasting data on environmental drivers. These three pieces of data are combined to generate a series of sequential transition matrices that emulate a pattern of long-term change in environmental drivers. Realistic estimates of population persistence and extinction risk can be derived from stochastic permutations of such a model. We illustrate the steps of this analysis with data from two populations of Sarracenia purpurea growing in northern New England. Sarracenia purpurea is a perennial carnivorous plant that is potentially at risk of local extinction because of increased nitrogen deposition. Long-term monitoring records or models of environmental change can be used to generate time series of driver variables under different scenarios of changing environments. Both manipulative and natural experiments can be used to construct a linking function that describes how matrix parameters change as a function of the environmental driver. This synthetic modeling approach provides quantitative estimates of extinction probability that have an explicit mechanistic basis.
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Affiliation(s)
- Nicholas J Gotelli
- Department of Biology, University of Vermont, Burlington, Vermont 05405, USA.
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42
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Ramula S, Lehtilä K. Matrix dimensionality in demographic analyses of plants: when to use smaller matrices? OIKOS 2005. [DOI: 10.1111/j.0030-1299.2005.13808.x] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Morris WF, Doak DF. HOW GENERAL ARE THE DETERMINANTS OF THE STOCHASTIC POPULATION GROWTH RATE ACROSS NEARBY SITES? ECOL MONOGR 2005. [DOI: 10.1890/03-4116] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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44
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Freedman AH, Portier KM, Sunquist ME. Life history analysis for black bears (Ursus americanus) in a changing demographic landscape. Ecol Modell 2003. [DOI: 10.1016/s0304-3800(03)00171-6] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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46
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Oli MK, Dobson FS. The relative importance of life-history variables to population growth rate in mammals: Cole's prediction revisited. Am Nat 2003; 161:422-40. [PMID: 12699222 DOI: 10.1086/367591] [Citation(s) in RCA: 160] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
The relative importance of life-history variables to population growth rate (lambda) has substantial consequences for the study of life-history evolution and for the dynamics of biological populations. Using life-history data for 142 natural populations of mammals, we estimated the elasticity of lambda to changes in age at maturity (alpha), age at last reproduction (omega), juvenile survival (Pj), adult survival (Pa), and fertility (F). Elasticities were then used to quantify the relative importance of alpha, omega, Pj, Pa, and F to lambda and to test theoretical predictions regarding the relative influence on lambda of changes in life-history variables. Neither alpha nor any other single life-history variable had the largest relative influence on lambda in the majority of the populations, and this pattern did not change substantially when effects of phylogeny and body size were statistically removed. Empirical support for theoretical predictions was poor at best. However, analyses of elasticities on the basis of the magnitude (F) and onset (alpha) of reproduction revealed that alpha, followed by F, had the largest relative influence on lambda in populations characterized by early maturity and high reproductive rates, or when F/alpha > 0.60. When maturity was delayed and reproductive rates were low, or when F/alpha < 0.15, survival rates were overwhelmingly most influential, and reproductive parameters (alpha and F) had little relative influence on lambda. Population dynamic consequences of likely responses of biological populations to perturbations in life-history variables are examined, and predictions are made regarding the numerical dynamics of age-structured populations on the basis of values of the F/alpha ratio.
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Affiliation(s)
- Madan K Oli
- Department of Wildlife Ecology and Conservation, University of Florida, Gainesville, Florida 32611-0430, USA.
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47
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Godfray HCJ, Rees M. Population growth rates: issues and an application. Philos Trans R Soc Lond B Biol Sci 2002; 357:1307-19. [PMID: 12396521 PMCID: PMC1693033 DOI: 10.1098/rstb.2002.1131] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Current issues in population dynamics are discussed in the context of The Royal Society Discussion Meeting 'Population growth rate: determining factors and role in population regulation'. In particular, different views on the centrality of population growth rates to the study of population dynamics and the role of experiments and theory are explored. Major themes emerging include the role of modern statistical techniques in bringing together experimental and theoretical studies, the importance of long-term experimentation and the need for ecology to have model systems, and the value of population growth rate as a means of understanding and predicting population change. The last point is illustrated by the application of a recently introduced technique, integral projection modelling, to study the population growth rate of a monocarpic perennial plant, its elasticities to different life-history components and the evolution of an evolutionarily stable strategy size at flowering.
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Affiliation(s)
- H Charles J Godfray
- NERC Centre for Population Biology and Department of Biological Sciences, Imperial College at Silwood Park, Ascot, Berkshire SL5 7PY, UK.
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48
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Abstract
Matrix population models are widely applied in conservation ecology to help predict future population trends and guide conservation effort. Researchers must decide upon an appropriate level of model complexity, yet there is little theoretical work to guide such decisions. In this paper we present an analysis of a stage-structured model, and prove that the model's structure can be simplified and parameterised in such a way that the long-term growth rate, the stable-stage distribution and the generation time are all invariant to the simplification. We further show that for certain structures of model the simplified models require less effort in data collection. We also discuss features of the models which are not invariant to the simplification and the implications of our results for the selection of an appropriate model. We illustrate the ideas using a population model for short-tailed shearwaters (Puffinus tenuirostris). In this example, model simplification can increase parameter elasticity, indicating that an intermediate level of complexity is likely to be preferred.
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49
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Rees M, Rose KE. Evolution of flowering strategies in Oenothera glazioviana: an integral projection model approach. Proc Biol Sci 2002; 269:1509-15. [PMID: 12137582 PMCID: PMC1691055 DOI: 10.1098/rspb.2002.2037] [Citation(s) in RCA: 60] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The timing of reproduction is a key determinant of fitness. Here, we develop parameterized integral projection models of size-related flowering for the monocarpic perennial Oenothera glazioviana and use these to predict the evolutionarily stable strategy (ESS) for flowering. For the most part there is excellent agreement between the model predictions and the results of quantitative field studies. However, the model predicts a much steeper relationship between plant size and the probability of flowering than observed in the field, indicating selection for a 'threshold size' flowering function. Elasticity and sensitivity analysis of population growth rate lambda and net reproductive rate R(0) are used to identify the critical traits that determine fitness and control the ESS for flowering. Using the fitted model we calculate the fitness landscape for invading genotypes and show that this is characterized by a ridge of approximately equal fitness. The implications of these results for the maintenance of genetic variation are discussed.
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Affiliation(s)
- Mark Rees
- Department of Biological Sciences and Natural Environment Research Council Centre for Population Biology, Imperial College, Silwood Park, Ascot, Berkshire SL5 7PY, UK.
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50
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Rose KE, Rees M, Grubb PJ. Evolution in the real world: stochastic variation and the determinants of fitness in Carlina vulgaris. Evolution 2002; 56:1416-30. [PMID: 12206242 DOI: 10.1111/j.0014-3820.2002.tb01454.x] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Empirical studies of life histories often ignore stochastic variation, despite theoretical demonstrations of its potential impact on life-history evolution. Here we use a novel approach to explore the effects of stochastic variation on life-history evolution and estimate the selection pressures operating on the monocarpic perennial Carlina vulgaris, in which flowering may be delayed by up to eight years. The approach is novel in that we use modern theoretical techniques to estimate selection pressures and the fitness landscape from a fully parameterised individual-based model. These approaches take into account temporal variation in demographic rates and density dependence. Analysis of 16 years' data revealed significant temporal variation in growth, mortality, and recruitment in our study population. Flowering was strongly size dependent and, unusually for such a species, also age dependent. Individual-based models of the flowering strategy, parameterized using field data, consistently underestimated the size at flowering, when temporal variation in demographic rates was ignored. In contrast, models that incorporated temporal variation in growth, mortality, and recruitment predicted sizes at flowering not significantly different from those observed in the field. Temporal variation in mortality, which had the largest effect on the flowering strategy, selected for increased size at flowering. An analytical approximation is presented to explain this result, extending the "1-year look-ahead criterion" presented in Rees et al. (2000). A fitness landscape generated by following the fate of rare mutant invaders with a broad range of alternative flowering strategies demonstrated that the observed parameters were adaptive. However, the fitness landscape reveals that approximately equal fitness is achieved by a broad range of strategies, providing a mechanism for the maintenance of genetic variation. To understand how the different parameters that defined our models determine the fitness of rare mutants, we numerically estimated the elasticities and sensitivities of mutant fitness. This demonstrated strong selection on a number of the parameters. Elasticities and sensitivities estimated in constant and random environments were significantly positively correlated, and both were negatively related to the standard error of the parameter. This last result is surprising and, we argue, reflects the genetic and phenotypic responses to selection.
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Affiliation(s)
- Karen E Rose
- Imperial College and Natural Environment Research Council Centre for Population Biology, Ascot, Berkshire, United Kingdom.
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